The present invention pertains in general to neural networks for use with optimization of plants and, more particularly, to the use of Bayesian-trained neural networks for optimization and control.
In general, modeling techniques for a plant involve the generation of some type of model. This is typically done utilizing a single model, either a linear model or a non-linear model. However, another technique of generating a model is to utilize a plurality of models that can be utilized to define a predicted vector output y(t) of values y1(t), y2(t), . . . , yq(t) as a function of an input vector x(t) of values x1(t), x2(t), . . . , xp(t). For the purposes of this application, a vector in the text shall be defined in bold and in equation form shall be defined with an overstrike arrow.
Given a set n of measured process data points:
D=({right arrow over (x)}1, {right arrow over (y)}1)=({right arrow over (x)}(1), {right arrow over (y)}(1)), ({right arrow over (x)}(2), {right arrow over (y)}(2)), . . . , ({right arrow over (x)}(n), {right arrow over (y)}(n))xe2x80x83xe2x80x83(1)
and assuming that an underlying mapping exists with the following relationship:
{right arrow over (y)}=F({right arrow over (x)})xe2x80x83xe2x80x83(2)
exists, a stochastical method for generating y(t) with respect to x(t) can be defined by averaging over many (non-linear) regression models F(w). Given x(t), Fx(t) is approximated via a stochastic neural network training algorithm (non-linear regression) to the set of functions F(w)x(t), with xe2x80x9cwxe2x80x9d being the index for the number of models, by fitting to the dataset (x(t), y(t)) in the dataset D. However, this only provides a forward predictive model and does not facilitate the use thereof for optimization or control purposes.
The present invention disclosed and claimed herein comprises a method for optimizing a system in which a plant is provided for optimization. A training network having an input layer for receiving inputs to the plant, an output layer for outputting predicted outputs, and a hidden layer for storing a learned representation of the plant for mapping the input layer to the output layer is also provided. A method for training the neural network in utilizing the stochastical method of a Bayesian-type is provided.
In another aspect of the present invention, a method utilizing the network in an optimization mode in feedback from the output of the plant to the input of the plant to optimize the output with respect to the input via the stochastical Bayesian method is provided.